Materials where crystal structure and electronic structure have different quasi-dimensionality

We theoretically study materials, such as LaTe3, in which the effective dimensionality of the crystal structure is quasi-two-dimensional while the electronic structure is quasi-one-dimensional. We show this by using a basis of electronic states that are maximally localized both in space and time. Unlike maximally localized Wannier functions, these orbitals have the property that their spread in space is minimally changing over time. We find that in such basis, relevant Te p-like electron orbitals evolve along one-dimensional chains within the LaTe3 plane (other p-like orbitals disperse in the perpendicular direction). We also find large, but less pronounced, quasi-one-dimensionality of electronic structure in NbS3. Interestingly, in NbS3 p-like orbitals on S tend to evolve along one-dimensional chains perpendicular to the ones formed by d-like Nb orbitals. We related these findings to the charge density wave state in both LaTe3 and NbS3. When we apply our approach to graphene, black phosphorene, and MoS2 we find that all three have very isotropic quasi-two-dimensional electronic structures (unlike LaTe3 and NbS3).